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http://dx.doi.org/10.4134/BKMS.2014.51.2.555

EXTENSIONS OF STRONGLY π-REGULAR RINGS  

Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
Kose, Handan (Department of Mathematics Ahi Evran University)
Kurtulmaz, Yosum (Department of Mathematics Bilkent University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.2, 2014 , pp. 555-565 More about this Journal
Abstract
An ideal I of a ring R is strongly ${\pi}$-regular if for any $x{\in}I$ there exist $n{\in}\mathbb{N}$ and $y{\in}I$ such that $x^n=x^{n+1}y$. We prove that every strongly ${\pi}$-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any $x{\in}I$ there exist two distinct m, $n{\in}\mathbb{N}$ such that $x^m=x^n$. Furthermore, we prove that an ideal I of a ring R is periodic if and only if I is strongly ${\pi}$-regular and for any $u{\in}U(I)$, $u^{-1}{\in}\mathbb{Z}[u]$.
Keywords
strongly ${\pi}$-regular ideal; B-ideal; periodic ideal;
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